Magnetic resonance imaging (MRI) is a very powerful tool in research and diagnostics. It comprises immerging a body in a static magnetic field B0 for aligning nuclear spins thereof; exposing it to a transverse, circularly-polarized radio-frequency (RF) pulse B1 at a resonance frequency known as the “Larmor frequency” for flipping said nuclear spins by a predetermined angle; and detecting a signal emitted by flipped nuclear spins, from which an image of the body can be reconstructed. Here, “transverse” means that the polarization plane of the RF pulse is perpendicular to the static magnetic field B0, which is conventionally assumed to be aligned along a “z” axis.
There is a trend to move towards higher and higher static magnetic fields in order to improve the spatial resolution of MRI. For example, magnetic fields of 1.5 T (Tesla) are currently used in clinical practice, 3 T is the highest field used in commercial apparatuses, and research systems can operate at more than 7 T. However, as the strength of the static magnetic field increases, the wavelength of the radio-frequency pulse decreases and its amplitude distribution within the body to be imaged becomes less homogeneous.
Radio-frequency pulsed field inhomogeneities already introduce significant artifacts at 3 T. At 7 T, the Larmor frequency of protons is about 298 MHz, which corresponds to a wavelength around 14 cm in the human brain, i.e. a size comparable to that of a human head. In these conditions, the radio-frequency field spatial distribution is so inhomogeneous that images e.g. of a human brain obtained with standard techniques can become very difficult to interpret.
The B1 inhomogeneity problem is so important that it could hinder further developments of high-resolution MRI.
A great number of techniques have been developed in order to compensate for B1 inhomogeneity or, more generally, in order to excite nuclear spins according to a uniform excitation pattern.
Parallel transmission consists in using a plurality of antennas to generate the radio-frequency pulsed field B1. In “static” parallel transmission (“RF shimming”) the amplitude and initial phase on each antenna are adjusted in order to homogenize the RF field by interference. Instead “dynamic” parallel transmission, e.g. in the so-called “Transmit SENSE” technique [1], does not aim at homogenizing the instantaneous radio-frequency field, but only the resulting spin flip angle. In other words, the field may stay inhomogeneous at some given instant, but the temporal variation of the radio-frequency field finally yields the desired excitation pattern. With respect to static “RF shimming”, dynamic parallel transmission allows homogenizing the flip angle over a much larger volume and reducing the electric energy left in the body as heat. However, all parallel transmission techniques have the drawback of adding hardware complexity. If parallel transmission is used as the sole strategy for counteracting B1 inhomogeneity, either very complex excitation coils are required or a significant residual inhomogeneity has to be tolerated.
The “three-dimensional tailored pulses” approach [2, 3] uses time-varying magnetic gradients to navigate in the spatial-frequency domain (“k-space”) along a predetermined trajectory whilst transmitting RF pulses.
In particular, document [2] relates to a method using a k-space trajectory in the form of a stack of spirals for achieving uniform excitation (i.e. flipping) of the spins within a region of interest of a body immerged in a uniform B0 field. This method is penalized by lengthy RF pulse durations, making it impractical for clinical applications and bringing B0-inhomogeneity and relaxation issues up front.
Document [3] describes a method using “spokes” trajectories with a static magnetic field gradient in a given direction to perform slice selection. This method only addresses flip-angle homogenization in the slice plane, and assumes B1-inhomogeneities to be insignificant through the selected slice.